Math question: How to compute the area of polygons

[Jim Hurley]

>
>Message: 6
>Date: Tue, 18 Mar 2003 10:06:57 +0100
>Subject: Math question: How to compute the area of polygons
>From: malte.brill at t-online.de (Malte Brill)
>To: <use-revolution at lists.runrev.com>
>Reply-To: use-revolution at lists.runrev.com
>
>Hi List,
>
>
>this one goes out to the math experts.
>How does one compute the area ( I hope it is the correct Term for
>flaecheninhalt in german) of a polygon with n sides.
>
>(That would get me started.)
>
>I want to extract all lines of 2 polygons by analysing their points,
>evaluate the area of each of them with some magic formula I don´t know ;-)
>and to figure out the area of the smallest polygon surrounding both of them.
>
>Any help will be greatly apprecheated!
>
>Regards,
>
>Malte
>

Hi Malte,

I'm not quite sure what you have in mind. Are these "regular" 
polygons? But the following might help get you started.

Put a list of points (x,y  coordinates) which defined the polygon 
into field 1. The run the following:

on mouseUp
   put field 1 into tList
   put 0 into area
   put  line 1 of tList into pOld
   repeat with i = 1 to the number of lines in tList
     put  line i of tList into  pNew
     add thisToArea(pNew,pOld) to area
     put pNew into pOld
   end repeat
   put area
end mouseUp

function thisToArea ptNew,ptOld
   put item 1 of ptNew into xNew
   put item 2 of ptNew into yNew
   put item 1 of ptOld into xOld
   put item 2 of ptOld into yOld
   return -(xNew - xOld)*(yNew + yOld)/2
end thisToArea

The area will be found in the message box. For example if field 1 
contains the following:

0,0
100,0
100,100
0,100
0,0

The area should be 10,000

Depending on what you have in mind, this might be much easier using 
Turtle Graphics.

Hope this gets you going.
Jim